In common with other ccTLDs there are some restrictions on which names you can register. These restrictions apply regardless of your eligibility.

Length of name

An IE domain may not be longer than 255 characters in length as per RFC-1035

Irish domain names with 2 characters are allowed but 2 letter domains are not.

The only IE domain with two letters (ul.ie) predates the establishment of the IEDR policy.

Offensive Names

3.4: The proposed domain name must not be offensive or contrary to public policy or generally accepted principles of morality.

The Irish domain registry naming policy includes this specific reference which is open to interpretation by the registry.

Place Names (Geographical)

To quote the Irish domain registry:

3.6: The proposed domain name must not contravene the geographical name regulation. This regulation requires that no domain name may consist of geographical name(s), word(s) or description(s), or a combination of such, followed by .ie, which in the view of the Registry would be likely to be misleading if registered in the name of the applicant, or if registered would be likely to infer or to imply that the applicant had exclusive or certain rights emanating from such a domain name.

These names, which can most often be defined as names that appear on official maps, are only registered to relevant local authorities. The Registry will not be involved in arrangements between local authorities and third parties regarding the use of the domain name. Quasi-geographical names that do not appear on official maps, such as Leeside, Bayside, Liffey Valley etc. are usually acceptable domain name applications from non-local authority applicants. Applications comprising corporate names, Trade Marks etc. and which include a (real) geographical name are usually compelled to include the "product" name in the domain name. For example, Westmeath Mountaineering Products would be obliged to include "mountaineering", or a derivation, at a minimum, in their domain name.

However, you may register a domain name based on a placename if you can get the written authorisation of the local authority.